The present invention relates to volume calculating apparatus and recording medium for calculating a volume of a body of rotation or a three-dimensional shape, and more particularly to such volume calculating apparatus and recording medium for calculating a volume of a body of rotation produced when a predetermined figure is rotated around a rotational axis or for calculating a volume of a solid body by analyzing a cross-sectional area of the solid body.
Conventionally, some software applications executed by a computer have been developed which have the functions of performing a function calculation, calculating an integrated value and displaying a corresponding solution, or displaying a graph based on input functional expression data, and displaying a range of its integration in a different color or display pattern.
A graph function calculator having a graph creating and displaying functions is used in a scene of education and/or/in engineer""s technical calculations. The graph function calculator contains various function operating programs which create and display a graph based on an input mathematical expression and/or an input table of numerals.
The software applications and/or graph function calculators, however, only draw graphs, display solutions of function calculation, and display ranges of integration recognizably, but do not display processes for obtaining those solutions. Leaning on integration performed in a site of education covers not only calculation of an area for a graph represented by a function expression, but also production of a body of rotation by rotating a graph expressed by a functional expression around an axis and calculation of the volume of the body of rotation. The learning further includes a volume calculation in which when the rotational axis is not parallel to a coordinate axis, the functional expression and the rotational axis are linearly transformed based on a rotary matrix so as to be parallel to the coordinate axis, and in which then the volume of the body of rotation is calculated based on the transformed functional expression and rotational axes.
In the calculation of the volume, not only the volume of a body of rotation but also the volume of a solid body can be calculated by integrating a functional expression indicative of a cross-sectional area concerned. However, it is not easy to draw cross-sectional shapes of the solid body as viewed in various directions. This greatly hinders the understanding of analysis of a cross-sectional area of the solid body.
It is therefore an object of the present invention to provide a volume calculating apparatus and a recording medium capable of displaying a body of rotation produced when a predetermined figure (a graph of a function, a drawn figure or the like) is rotated around a predetermined rotational axis.
Another object of the present invention is to provide a volume calculating apparatus and a recording medium capable of calculating a volume of a body of rotation produced when a predetermined figure (a graph of a function, a created figure or the like) is rotated around a predetermined rotational axis.
A further object of the present invention is to provide a volume calculating apparatus and a recording medium capable of calculating a volume of any solid body.
A still further object of the present invention is to provide a volume calculating apparatus and a recording medium capable of clearly displaying a cross section of any solid body in any direction.